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Mesh refinement processes based on the generalized bisection of simplices. (English) Zbl 0574.65133
Mesh-refinement processes based on the generalized bisection of simplices are discussed and characterized in the context of the general theory of W. C. Rheinboldt [ibid. 17, 766-778 (1980; Zbl 0472.65009)]. Then it is proved that such processes allow the construction of sequences of naturally smooth conforming and nested nonuniform meshes. In fact it is shown that there exists a generalized mesh-refinement operator that for any conforming triangulation \(\Delta\) and for any \(V\subset \Delta\), produces a nested, smooth, conforming triangulation \(\Delta^*\) containing successors of all elements of V and such that the minimum cell-size of \(\Delta^*\) is bounded from below by half the minimum cell- size of \(\Delta\). Two conforming mesh-refinement algorithms that allow the selective refinement of computational triangulations are explicitly given.

65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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